<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We consider a class of double exponential sums studied in a paper of Sinai and Ulcigrai. They proved a linear bound for these sums along the sequence of denominators in the continued fraction expansion of α, provided α is badly-approximable. We provide a proof of a result, which includes a simple proof of their theorem, and which applies for all irrational α.</p></abstract>

We consider a class of double exponential sums studied in a paper of Sinai and Ulcigrai. They proved a linear bound for these sums along the sequence of denominators in the continued fraction expansion of α, provided α is badly-approximable. We provide a proof of a result, which includes a simple proof of their theorem, and which applies for all irrational α.

Upper Bounds for Double Exponential Sums Along a Subsequence

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Upper Bounds for Double Exponential Sums Along a Subsequence"}

We consider a class of double exponential sums studied in a paper of Sinai and Ulcigrai. They proved a linear bound for these sums along the sequence of...

Upper Bounds for Double Exponential Sums Along a Subsequence

Published Online: Jan 30, 2018

Page range: 11 - 24

Received: Nov 01, 2015

Accepted: Oct 10, 2016

DOI: https://doi.org/10.1515/udt-2017-0012

Keywords
continued fraction, badly-approximable α, double-exponential sum, discrepancy, Koksma-Hlawka inequality, Ostrowski expansion

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Upper Bounds for Double Exponential Sums Along a Subsequence

Published Online: Jan 30, 2018

Page range: 11 - 24

Received: Nov 01, 2015

Accepted: Oct 10, 2016

DOI: https://doi.org/10.1515/udt-2017-0012

Keywordscontinued fraction, badly-approximable α, double-exponential sum, discrepancy, Koksma-Hlawka inequality, Ostrowski expansion

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
continued fraction, badly-approximable α, double-exponential sum, discrepancy, Koksma-Hlawka inequality, Ostrowski expansion